This is a simple proof, one of which i should know. However, I don\'t know it at

Question

This is a simple proof, one of which i should know. However, I don't know it at all on why this identity is true. If it is a provable identity, can someone show me the proof. If it is not, can someone explain to me why this is true, or show by some diagram?

I'm trying to prove that (~X*Y) + ( X + ~Y ) = ~X*Y

~ is NOT
* is AND
+ is OR

Please use any justification or property used, and please show each step. Thank you guys

Its important for me to know this because i keep seeing it, and just memorizing it would be difficult for me. I need to understand WHY that is true. thanks guys.

Explanation / Answer

I do not believe the identity you have provided is true. Adding some parenthesis (to ensure no precedence issues arise) and verbalizing it rather than using shorthand you get:

[(NOT X) AND Y] OR [X OR (NOT Y)] = (NOT X) AND Y

Now see if any of the four possible cases [(0,0) (0,1) (1,0) (1,1)] result in an incorrect conclusion:

Let X be false (0)
Let Y be false (0)

[(NOT 0) AND 0] OR [0 OR (NOT 0)] = (NOT 0) AND 0

[1 AND 0] OR [0 OR 1] = 1 AND 0

0 OR 1 = 0

1 = 0 ----> WRONG!

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